Ch 03: Motion in Two or Three Dimensions

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 03: Motion in Two or Three Dimensions

Problem 22c

Chapter 3, Problem 22c

A 124 kg balloon carrying a 22 kg basket is descending with a constant downward velocity of 20.0 m/s. A 1.0 kg stone is thrown from the basket with an initial velocity of 15.0 m/s perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. That person sees the stone hit the ground 5.00 s after it was thrown. Assume that the balloon continues its downward descent with the same constant speed of 20.0 m/s. At the instant the rock hits the ground, how far is it from the basket?

Verified step by step guidance

First, determine the vertical distance the stone travels. Since the stone is thrown perpendicular to the balloon's descent, its initial vertical velocity is the same as the balloon's, which is 20.0 m/s downward. Use the formula for distance:

d = v t

, where

v

is the velocity and

t

is the time.

Calculate the vertical distance the stone falls in 5.00 seconds using the formula:

d = v t

. Substitute

v

with 20.0 m/s and

t

with 5.00 s.

Next, determine the horizontal distance traveled by the stone. The stone is thrown with an initial horizontal velocity of 15.0 m/s. Use the formula for horizontal distance:

d = v t

, where

v

is the horizontal velocity and

t

is the time.

Calculate the horizontal distance the stone travels in 5.00 seconds using the formula:

d = v t

. Substitute

v

with 15.0 m/s and

t

with 5.00 s.

Finally, use the Pythagorean theorem to find the total distance from the basket to the stone when it hits the ground. The vertical and horizontal distances form a right triangle, so the total distance is given by:

d = \sqrt{d^{2} + d^{2}}

, where

d

represents the vertical and horizontal distances.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

15m

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Relative Velocity

Relative velocity is the velocity of an object as observed from a particular frame of reference. In this problem, the stone's velocity is given relative to the basket, which is itself moving. Understanding how to convert this relative velocity to an absolute velocity with respect to the ground is crucial for solving the problem.

Projectile Motion

Projectile motion describes the motion of an object thrown into the air, subject to only the acceleration of gravity. The stone, once thrown, follows a projectile path. Analyzing its horizontal and vertical components separately allows us to determine its trajectory and final position when it hits the ground.

Vector Addition

Vector addition is the process of combining vectors to determine a resultant vector. In this scenario, the stone's velocity relative to the basket and the basket's velocity relative to the ground must be added vectorially to find the stone's velocity relative to the ground, which is essential for calculating the stone's displacement.

Recommended video:

Guided course

07:30

Vector Addition By Components

Related Practice

Textbook Question

The earth has a radius of 6380 km and turns around once on its axis in 24 h. If a_rad at the equator is greater than g, objects will fly off the earth's surface and into space. (We will see the reason for this in Chapter 5.) What would the period of the earth's rotation have to be for this to occur?

Textbook Question

In a carnival booth, you can win a stuffed giraffe if you toss a quarter into a small dish. The dish is on a shelf above the point where the quarter leaves your hand and is a horizontal distance of 2.1 m from this point (Fig. E3.19). If you toss the coin with a velocity of 6.4 m/s at an angle of 60° above the horizontal, the coin will land in the dish. Ignore air resistance. What is the vertical component of the velocity of the quarter just before it lands in the dish?

views

Textbook Question

A model of a helicopter rotor has four blades, each 3.40 m long from the central shaft to the blade tip. The model is rotated in a wind tunnel at 550 rev/min. What is the linear speed of the blade tip, in m/s?

Textbook Question

The earth has a radius of 6380 km and turns around once on its axis in 24 h. What is the radial acceleration of an object at the earth's equator? Give your answer in m/s² and as a fraction of g.

views

Textbook Question

A 124 kg balloon carrying a 22 kg basket is descending with a constant downward velocity of 20.0 m/s. A 1.0 kg stone is thrown from the basket with an initial velocity of 15.0 m/s perpendicular to the path of the descending balloon, as measured relative to a person at rest in the basket. That person sees the stone hit the ground 5.00 s after it was thrown. Assume that the balloon continues its downward descent with the same constant speed of 20.0 m/s. How high is the balloon when the rock is thrown?

views

Textbook Question

A man stands on the roof of a 15.0-m-tall building and throws a rock with a speed of 30.0 m/s at an angle of 33.0° above the horizontal. Ignore air resistance. Calculate Draw x-t, y-t, v_x–t, and v_y–t graphs for the motion.

views